is not just," but the opposite, "some man is just," follows "not every man is not just," for it is necessary that some man should be just. In the case also of singulars, it is evident that if a man being questioned denies truly, he asserts also truly, as, "Is Socrates wise? No!" Socrates therefore is not a wise man. But in the case of universals, what is similarly asserted is not true, but the negation is true, as, "Is every man wise? No!" Every man therefore is not wise; for this is false, but this, "not every man then is wise," is true, and this is opposite, but that is contrary.
Opposites, however, as to indefinite nouns and verbs, as "non-man" and "non-just," may seem to be negations without a noun and verb, but they are not so, for the negation must always of necessity be either true or false, but he who says "non-man" does not speak more truly or falsely, but rather less, than he who says "man," except something be added. Still the assertion, "every non-man is just", does not signify the same as any one of those (propositions), nor the opposite to this, namely, "not every non-man is just;" but the assertion, "every one not just is not a man," means the same with, "no one is just who is not a man."
Nouns and verbs indeed, when transposed, have the same signification, as, "he is a white man," "he is a man white," for unless it be so, there will be many negations of the same thing, but it has been shown that there is one of one; of this, "he is a white man," there is the negation "he is not a white man," and of the other, "he is a man white," (except this be the same with "he is a white man,") the negation will either be "he is not, not a man white," or "he is not a man white." But the one is a negation of this, "he is not a man white," and the other of this, "he is a white man" (so that there will be two negations of one
